A scanner-less laser radar range imaging system is described in U.S. Pat. No. 4,935,616. The system described therein illuminates a scene object with an amplitude modulated laser source, wherein the amplitude modulation is in the range of 10MHz. The image capture portion of the system includes a micro-channel plate that is capable of modulating the optical signal reflected from the scene object. The phase shift of the intensity modulation reflected from the scene object can be calculated by capturing two images, one without modulating the optical signal, and another with the optical signal modulated by the micro-channel plate in phase with the same amplitude modulated frequency as used to modulate the laser source. Both images are registered spatially, and the difference between them is caused by the interference of the two modulating wave patterns, which produces a dc signal proportional to the phase shift. Once the phase shift has been established, range to the object can be computed.
Since the phase shift can only be determined modulo 27.pi. the resulting range can only be found to within one wavelength of the modulation of the laser. To calculate the range at each point in the image, the correct integer number of phase cycles must be added to each phase measurement; that is, the phase must be "unwrapped". It is therefore desirable to resolve the ambiguous (or wrapped) phase measurements to determine unambiguous (or unwrapped) phase.
The unambiguous phase, in turn, can be used to calculate unambiguous range. The aforementioned '616 patent suggests modulating the laser and receiver with different frequencies in order to produce two range images with different modulating frequencies. This would yield range unambiguous to within one wavelength of the wave whose frequency is the greatest common factor of the frequencies of the laser and receiver, which is a lower frequency than either of the two modulating frequencies. Even though this may reduce ambiguity problems in many situations, they still exist albeit on a smaller scale.
There are two main types of methods for solving the phase ambiguity problem: branch-cut methods and weighted least-squares methods.
Branch-cut methods (such as those described in Goldstein, Zebker, and Werner, "Satellite radar interferometry: two-dimensional phase unwrapping", Radio Science, Vol. 23, pp. 713-720, 1998; and Prati, Giani, and Leurati, "SAR interferometry: A 2-D phase unwrapping technique based on phase and absolute values informations", Proc. Int. Geoscience & Remote Sensing Symposium IGARSS 1990, Washington, D.C., pp. 2043-2046, 1990) use lines to connect phase inconsistencies (or residues). Branch-cut methods fail to perform adequately when the number of residues is high. They often resort to local averaging, which is undesirable because it can dampen high frequency information. Least-squares methods (such as those described in Ghiglia and Romero, "Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods", Journal of the Optical Society of America, Vol. 11, pp.107-117, 1994; and Pritt and Shipman, "Least-squares two dimensional phase unwrapping using FFT's", IEEE Transactions on Geoscience and Remote Sensing, Vol. 32, pp. 706-708, 1994) determine a phase finction that minimizes the error in the gradient estimates. If there are areas in the ambiguous phase image with a high noise content, nearby areas with a low noise content can be distorted by a least-squares phase unwrapping algorithm.